Answer:
x² -3x -28 = 0
Step-by-step explanation:
If the roots are -4 and 7, the factors are ...
... (x -(-4))·(x -7) = (x +4)(x -7)
and the equation with those zeros is ...
... (x +4)(x -7) = 0 = x² -3x -28
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Comment on such questions
If "a" is a root/zero/solution, then (x-a) is a factor of the quadratic expression whose value is zero. A quadratic will have 2 roots, so we can call them "p" and "q" and write the factored form as
... (x -p)(x -q) = 0
Expanding gives ...
... x² -(p+q)x +pq = 0
Comparing this to the generic equation ...
... ax² +bx +c = 0
we see that when the leading coefficient (a) is 1, then b=-(p+q), the opposite of the sum of the solutions; and c=pq, the product of the solutions. So, when you are given the two solutions as being -4 and +7, you can write the equation as
... x² -(-4+7)x +(-4)(7) = 0
... x² -3x -28 = 0
